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On the Existence of a Compact Generator on the Derived Category of a Noetherian Formal Scheme

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Abstract

In this paper, we prove that for a noetherian formal scheme \(\mathfrak X\), its derived category of sheaves of modules with quasi-coherent torsion homologies \(\boldsymbol{\mathsf{D}}_\mathsf{qct}(\mathfrak X)\) is generated by a single compact object. In an Appendix we prove that the category of compact objects in \(\boldsymbol{\mathsf{D}}_\mathsf{qct}(\mathfrak X)\) is skeletally small.

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Authors and Affiliations

  1. Departamento de Álxebra, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Leovigildo Alonso Tarrío, Ana Jeremías López & María J. Vale Gonsalves

  2. Departamento de Matemáticas, Esc. Sup. de Enx. Informática, Campus de Ourense, Universidade de Vigo, 32004, Ourense, Spain

    Marta Pérez Rodríguez

Authors
  1. Leovigildo Alonso Tarrío
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  2. Ana Jeremías López
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  3. Marta Pérez Rodríguez
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  4. María J. Vale Gonsalves
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Corresponding author

Correspondence to Leovigildo Alonso Tarrío.

Additional information

This work has been partially supported by Spain’s MEC and E.U.’s FEDER research projects MTM2005-05754 and MTM2008-03465.

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Alonso Tarrío, L., Jeremías López, A., Pérez Rodríguez, M. et al. On the Existence of a Compact Generator on the Derived Category of a Noetherian Formal Scheme. Appl Categor Struct 19, 865–877 (2011). https://doi.org/10.1007/s10485-009-9204-5

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  • DOI: https://doi.org/10.1007/s10485-009-9204-5

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